Asymptotic unbiased density estimators

Nicolas W. Hengartner; Éric Matzner-Løber

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 1-14
  • ISSN: 1292-8100

Abstract

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This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n = 50, where we see an improvement of as much as 20% over the traditionnal estimator.

How to cite

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Hengartner, Nicolas W., and Matzner-Løber, Éric. "Asymptotic unbiased density estimators." ESAIM: Probability and Statistics 13 (2009): 1-14. <http://eudml.org/doc/250655>.

@article{Hengartner2009,
abstract = { This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n = 50, where we see an improvement of as much as 20% over the traditionnal estimator. },
author = {Hengartner, Nicolas W., Matzner-Løber, Éric},
journal = {ESAIM: Probability and Statistics},
keywords = {Nonparametric density estimation; kernel smoother; asymptotic normality; bias reduction; confidence intervals; nonparametric density estimation; asymptotic normality},
language = {eng},
month = {2},
pages = {1-14},
publisher = {EDP Sciences},
title = {Asymptotic unbiased density estimators},
url = {http://eudml.org/doc/250655},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Hengartner, Nicolas W.
AU - Matzner-Løber, Éric
TI - Asymptotic unbiased density estimators
JO - ESAIM: Probability and Statistics
DA - 2009/2//
PB - EDP Sciences
VL - 13
SP - 1
EP - 14
AB - This paper introduces a computationally tractable density estimator that has the same asymptotic variance as the classical Nadaraya-Watson density estimator but whose asymptotic bias is zero. We achieve this result using a two stage estimator that applies a multiplicative bias correction to an oversmooth pilot estimator. Simulations show that our asymptotic results are available for samples as low as n = 50, where we see an improvement of as much as 20% over the traditionnal estimator.
LA - eng
KW - Nonparametric density estimation; kernel smoother; asymptotic normality; bias reduction; confidence intervals; nonparametric density estimation; asymptotic normality
UR - http://eudml.org/doc/250655
ER -

References

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